Do you play characters with Level Adjustment. If so, what are your experience playing characters with level adjustment?

There is a huge amount of variety amongst LA-adjusted characters, which is unsurprising given that there are surely more LA-adjusted races than there are non-LA ones. Asking what your experience playing a character with a level adjustment is is a bit like asking what your experience playing a Core race is or what your experience playing a race with a Dexterity penalty is, or something - it's going to vary massively from character to character.

The only thing that LA-adjusted races have in common is, well, obviously, the LA, and this means that they are all going to suffer what are largely the same drawbacks. Consequently, they tend to make poor spellcasters, and anything you do have which is tied to class level is going to lag behind other characters. These characters will probably tend to be defined more by their race; at low levels especially it's going to make up more of what they can do, and even later in their career the very high-LA races tend to be more unusual and therefore those characters may feel more unique, especially if they are amongst more "standard" races.

I've played a few +1 LA characters (Aasimars and Goliaths and the like) and these don't tend to feel terribly different to regular characters; they get a few bonuses but they lag behind a level in getting class features. Most things with a higher LA will start to play a bit more differently, but how will vary from race to race. An Astral Deva is not going to be the same as a Sylph or a Nightmare or a War Troll, for example.

Do LA-adjusted races make bad spellcasters? It's certain that they don't benefit from having higher level spells/slots, and their caster level is shot, but a lot of utility spells (Fly, Invisibility, Tongues, etc) are already available at low levels, and if they have a high spellcasting ability score, wouldn't that raise their spell save DC and give them bonus spells anyway?
So they don't get the stronger spells, and their damage spells/utilities don't do as much or last as long, but they'd be harder to resist and they'd get a fair few bonus spells to offset the missing ones by level?

The problem here is that you naturally gain more spells as you level and +2 or 4 to a casting stat may not be worth that. More importantly, you naturally gain more spell levels.

Just a quick thought experiment, a Wizard 2 with 20 Int versus a Wizard 3 with 18 Int:
The Wizard 2 has four 1st level spell slots. The Wizard 3 has three. But the Wizard 3 also has two 2nd level spell slots. He has more spell slots overall, and can be considered to have more powerful ones since he can now put +1 metamagic onto his 1st level spells and has access to many, many more spells than the Wizard 2.
Even if you bump that to 22 Int, it doesn't change much.
You'd have to be grabbing a +6 to your casting stat to make a +1 LA worth it, since you're missing out on access to spell levels, not just the number of spells per day.

As for the DCs, the Wizard 3 will get his feats sooner than the Wizard 2, so he can bump the DCs higher sooner. Even without that, the one or two point DC difference is offset again by the high level spells naturally having higher DCs.
Spell, and sometimes class, progression is more important than a bump in stats, as stats scale slowly and linearly, but spells progress exponentially and fairly quickly.

LA just ain't worth it 90% of the time for a primary caster. Gish, Bard/Ranger type casters, and martial classes do better with LA, though. This is mostly because they like having +2 to two different stats. Full casters don't care as much.

You do have to take the racial Hit Dice if they're present. No way around this, you absolutely must.

However, what you can do is level drain them away. This is rather cheesy, and most DM's will flat-out deny it, but it works. Get hit with negative levels equal to your HD-1 and fail the saves after 24 hours so the level loss becomes real. Now you're a 1HD creature. Taking a level in a class substitutes your 1 racial HD for that class level and there you go. It is possible to play a Centaur with 18 class levels as an ECL 20 character. 20 levels if LA Buyoff is allowed.

I'm going to have to remember that trick. Once in a while a higher op game comes around that basically demands a Gish or a caster, but this would be a trick if coupled with the right race and/or template to make more normal-ish sneaks or warriors remain viable for longer. =)

That said, I do frequently enjoy LA when I can get around/get away with keeping it form overly impacting the characters being awesome at the things there suppose to be awesome at. =)

So they don't get the stronger spells, and their damage spells/utilities don't do as much or last as long, but they'd be harder to resist and they'd get a fair few bonus spells to offset the missing ones by level?

Yes, but in general higher levels of spells greatly outweigh the other benefits - especially if you're looking at only a +2 to a stat for a +1 LA or similar (usually things don't give more than +4 per LA to any given stat). The extra stat boosts can keep such a character from being too bad and actually if you pick smart low-level spells it's not like you won't be able to contribute, but once you get a big LA you just won't be as good.

Some races give racial spellcasting and they tend to be more viable. Overall they're still a few levels behind so they're in a similar position but they can be a lot more "monstrous" and still at least doable. You're not going to want to play an Ettercap Druid, for example, because you're nine whole casting levels behind, which the meagre +4 Wis can't hope to make up for. However a Drider is ECL 10 and already casts like a L6 caster, so you're only four levels behind. That's a pretty big hit but you can see it as similar to a race with only +4 LA (Drider also has 6 racial HD) to get +4 or +6 to your mental stat (you can pick Cleric, Wizard or Sorcerer) and a whole host of other benefits. Because Driders are Large and have an NA bonus and extra Strength they might make decent gishes, for example, and gishes expect to lose a level of casting or two anyway - but they're still going to be poor as pure casters.

One exception is probably the Sylph which actually casts at a higher level than its HD, but it has a whopping +5 LA so that it's casting a level lower than its ECL. But casting only one level lower in exchange for flight and big Dex and Cha bonuses is not that bad a trade-off. Its weird rules also suggest that more HD = more casting so at high levels you can make an excellent gish by just taking Outsider HD which is full BAB and full casting, and maybe go into Abjurant Champion without ever taking any other class levels. (It's also a bit notorious because with LA buyoff you can eventually be casting above your level, though obviously LA buyoff is a bit of a variant anyway).

This is all in contrast to melee, where having a big Strength bonus and maybe Large, natural armour, natural weapons, etc, actually do balance out the loss of BAB and stuff. Having a lower BAB means slower iterative attacks and slower access to some feats and PrCs and things but that just isn't as important as higher levels of spells are. Meanwhile if you get a bite attack and a big Strength bonus your overall AB might actually be better, you might even be making more attacks (though your secondary weapon might be a bit weak) and you'll be doing more damage with each hit. It's why Dragon Disciple actually stacks up surprisingly well. Plus, you may be able to get things like Knockback or certain monstrous feats. There's not really much in the way of other options that being a monster might give you that benefit a spellcaster, and certainly not anywhere as much as higher levels of spells does.

Yeah. I play level-adjusted races a lot. I've found a few - mainly templates like Dark, Lolth-Touched, and Mineral Warrior - that are actually worth it. (Also Maugs. Maugs are awesome.)
Having done the math at great length recently, I find that most creatures with level adjustment justify at best half their listed level adjustment, and that adding their CR instead tends to more accurately represent what they bring to the table. Monster HD in anything other than Dragon or Outsider are generally crap, and can be as much of a tax on a character as the LA itself. At least it's not literally nothing, but still crap.

As others have said, LA is terrible for casters and (with a few exceptions) usually a poor choice for beatsticks. That said, it's possible to have a very enjoyable character even though you can't contribute in combat the way the rest of your party can.

Case in point, play a gold dragon sometime and see how many times flight, darkvision, water breathing, and immunity to fire allow you to have fun. Plus your party will never have to worry about starting campfires again.

+1, Sure. There's often something worthwhile in +1 races, as long as they have no RHD. +2 is a lot iffier unless buy-off is available. Nothing higher though unless I'm being really experimental and not all that concerned with survivability.